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.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
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.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        Click :ref:`here <sphx_glr_download_examples_scalable_plot_scalable_param_mdf.py>`
        to download the full example code

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_examples_scalable_plot_scalable_param_mdf.py:


Parametric scalable MDO problem - MDF
=====================================
We define a scalable problem based on two strongly coupled disciplines
and a weakly one, with the following properties:

- 3 shared design parameters,
- 2 local design parameters for the first strongly coupled discipline,
- 2 coupling variables for the first strongly coupled discipline,
- 4 local design parameters for the second strongly coupled discipline,
- 3 coupling variables for the second strongly coupled discipline.

We would like to solve this MDO problem by means of an MDF formulation.

.. GENERATED FROM PYTHON SOURCE LINES 35-45

.. code-block:: default

    from __future__ import annotations

    from gemseo.api import configure_logger
    from gemseo.api import create_scenario
    from gemseo.api import generate_n2_plot
    from gemseo.problems.scalable.parametric.problem import TMScalableProblem
    from matplotlib import pyplot as plt

    configure_logger()





.. rst-class:: sphx-glr-script-out

 .. code-block:: none


    <RootLogger root (INFO)>



.. GENERATED FROM PYTHON SOURCE LINES 46-48

Instantiation of the scalable problem
-------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 48-53

.. code-block:: default

    n_shared = 3
    n_local = [2, 4]
    n_coupling = [2, 3]
    problem = TMScalableProblem(n_shared, n_local, n_coupling)








.. GENERATED FROM PYTHON SOURCE LINES 54-56

Display the coupling structure
------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 56-58

.. code-block:: default

    generate_n2_plot(problem.disciplines, save=False, show=True)




.. image-sg:: /examples/scalable/images/sphx_glr_plot_scalable_param_mdf_001.png
   :alt: plot scalable param mdf
   :srcset: /examples/scalable/images/sphx_glr_plot_scalable_param_mdf_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 59-61

Solve the MDO using an MDF formulation
--------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 61-66

.. code-block:: default

    scenario = create_scenario(problem.disciplines, "MDF", "obj", problem.design_space)
    scenario.add_constraint("cstr_0", "ineq")
    scenario.add_constraint("cstr_1", "ineq")
    scenario.execute({"algo": "NLOPT_SLSQP", "max_iter": 100})





.. rst-class:: sphx-glr-script-out

 .. code-block:: none

        INFO - 14:44:43:  
        INFO - 14:44:43: *** Start MDOScenario execution ***
        INFO - 14:44:43: MDOScenario
        INFO - 14:44:43:    Disciplines: MainModel SubModel_0 SubModel_1
        INFO - 14:44:43:    MDO formulation: MDF
        INFO - 14:44:43: Optimization problem:
        INFO - 14:44:43:    minimize obj(x_local_0, x_local_1, x_shared)
        INFO - 14:44:43:    with respect to x_local_0, x_local_1, x_shared
        INFO - 14:44:43:    subject to constraints:
        INFO - 14:44:43:       cstr_0(x_local_0, x_local_1, x_shared) <= 0.0
        INFO - 14:44:43:       cstr_1(x_local_0, x_local_1, x_shared) <= 0.0
        INFO - 14:44:43:    over the design space:
        INFO - 14:44:43:    |                               Parameter space                                |
        INFO - 14:44:43:    +-----------+-------------+-------+-------------+-------+----------------------+
        INFO - 14:44:43:    | name      | lower_bound | value | upper_bound | type  | Initial distribution |
        INFO - 14:44:43:    +-----------+-------------+-------+-------------+-------+----------------------+
        INFO - 14:44:43:    | x_local_0 |      0      |  0.5  |      1      | float |                      |
        INFO - 14:44:43:    | x_local_0 |      0      |  0.5  |      1      | float |                      |
        INFO - 14:44:43:    | x_local_1 |      0      |  0.5  |      1      | float |                      |
        INFO - 14:44:43:    | x_local_1 |      0      |  0.5  |      1      | float |                      |
        INFO - 14:44:43:    | x_local_1 |      0      |  0.5  |      1      | float |                      |
        INFO - 14:44:43:    | x_local_1 |      0      |  0.5  |      1      | float |                      |
        INFO - 14:44:43:    | x_shared  |      0      |  0.5  |      1      | float |                      |
        INFO - 14:44:43:    | x_shared  |      0      |  0.5  |      1      | float |                      |
        INFO - 14:44:43:    | x_shared  |      0      |  0.5  |      1      | float |                      |
        INFO - 14:44:43:    +-----------+-------------+-------+-------------+-------+----------------------+
        INFO - 14:44:43: Solving optimization problem with algorithm NLOPT_SLSQP:
        INFO - 14:44:43: ...   0%|          | 0/100 [00:00<?, ?it]
     WARNING - 14:44:43: MDAJacobi has reached its maximum number of iterations but the normed residual 628.5348041278223 is still above the tolerance 1e-06.
        INFO - 14:44:43: ...   2%|▏         | 2/100 [00:00<00:00, 631.85 it/sec, obj=0.5]
     WARNING - 14:44:43: MDAJacobi has reached its maximum number of iterations but the normed residual 855.939250180759 is still above the tolerance 1e-06.
     WARNING - 14:44:43: MDAJacobi has reached its maximum number of iterations but the normed residual 1222.112924405924 is still above the tolerance 1e-06.
        INFO - 14:44:43: ...   4%|▍         | 4/100 [00:00<00:00, 306.86 it/sec, obj=0.5]
     WARNING - 14:44:43: MDAJacobi has reached its maximum number of iterations but the normed residual 1385.5049620986567 is still above the tolerance 1e-06.
     WARNING - 14:44:44: MDAJacobi has reached its maximum number of iterations but the normed residual 1733.2178166635606 is still above the tolerance 1e-06.
        INFO - 14:44:44: ...   6%|▌         | 6/100 [00:00<00:00, 202.13 it/sec, obj=0.5]
     WARNING - 14:44:44: MDAJacobi has reached its maximum number of iterations but the normed residual 1809.1058564937541 is still above the tolerance 1e-06.
     WARNING - 14:44:44: MDAJacobi has reached its maximum number of iterations but the normed residual 1810.0817661089236 is still above the tolerance 1e-06.
        INFO - 14:44:44: ...   8%|▊         | 8/100 [00:00<00:00, 150.66 it/sec, obj=0.5]
     WARNING - 14:44:44: MDAJacobi has reached its maximum number of iterations but the normed residual 1804.117512802312 is still above the tolerance 1e-06.
     WARNING - 14:44:44: MDAJacobi has reached its maximum number of iterations but the normed residual 1781.4230266840048 is still above the tolerance 1e-06.
        INFO - 14:44:44: ...  10%|█         | 10/100 [00:00<00:00, 120.36 it/sec, obj=0.5]
     WARNING - 14:44:44: MDAJacobi has reached its maximum number of iterations but the normed residual 1646.1968290578134 is still above the tolerance 1e-06.
     WARNING - 14:44:44: MDAJacobi has reached its maximum number of iterations but the normed residual 909.2480409657202 is still above the tolerance 1e-06.
        INFO - 14:44:44: ...  12%|█▏        | 12/100 [00:00<00:00, 100.13 it/sec, obj=0.5]
     WARNING - 14:44:44: MDAJacobi has reached its maximum number of iterations but the normed residual 725.9807159973328 is still above the tolerance 1e-06.
     WARNING - 14:44:44: MDAJacobi has reached its maximum number of iterations but the normed residual 724.9413769402323 is still above the tolerance 1e-06.
        INFO - 14:44:44: ...  14%|█▍        | 14/100 [00:01<00:01, 85.75 it/sec, obj=0.5]
     WARNING - 14:44:44: MDAJacobi has reached its maximum number of iterations but the normed residual 726.784699893992 is still above the tolerance 1e-06.
        INFO - 14:44:44: ...  15%|█▌        | 15/100 [00:01<00:01, 80.00 it/sec, obj=0.5]
        INFO - 14:44:44: Optimization result:
        INFO - 14:44:44:    Optimizer info:
        INFO - 14:44:44:       Status: None
        INFO - 14:44:44:       Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO Stopped the driver
        INFO - 14:44:44:       Number of calls to the objective function by the optimizer: 15
        INFO - 14:44:44:    Solution:
        INFO - 14:44:44:       The solution is feasible.
        INFO - 14:44:44:       Objective: 0.670463878639397
        INFO - 14:44:44:       Standardized constraints:
        INFO - 14:44:44:          cstr_0 = [-0.01693211 -5.62972098]
        INFO - 14:44:44:          cstr_1 = [-1.05472950e+00  2.22044605e-16 -1.81142650e+00]
        INFO - 14:44:44:       +----------------------------------------------------------------------------------------------+
        INFO - 14:44:44:       |                                       Parameter space                                        |
        INFO - 14:44:44:       +-----------+-------------+-----------------------+-------------+-------+----------------------+
        INFO - 14:44:44:       | name      | lower_bound |         value         | upper_bound | type  | Initial distribution |
        INFO - 14:44:44:       +-----------+-------------+-----------------------+-------------+-------+----------------------+
        INFO - 14:44:44:       | x_local_0 |      0      |   0.5931064439648591  |      1      | float |                      |
        INFO - 14:44:44:       | x_local_0 |      0      |           1           |      1      | float |                      |
        INFO - 14:44:44:       | x_local_1 |      0      |           0           |      1      | float |                      |
        INFO - 14:44:44:       | x_local_1 |      0      |   0.9546530639347032  |      1      | float |                      |
        INFO - 14:44:44:       | x_local_1 |      0      |           0           |      1      | float |                      |
        INFO - 14:44:44:       | x_local_1 |      0      | 4.985109760672119e-16 |      1      | float |                      |
        INFO - 14:44:44:       | x_shared  |      0      | 5.297941653541373e-17 |      1      | float |                      |
        INFO - 14:44:44:       | x_shared  |      0      |           0           |      1      | float |                      |
        INFO - 14:44:44:       | x_shared  |      0      | 2.001779104424825e-16 |      1      | float |                      |
        INFO - 14:44:44:       +-----------+-------------+-----------------------+-------------+-------+----------------------+
        INFO - 14:44:44: *** End MDOScenario execution (time: 0:00:01.268875) ***

    {'max_iter': 100, 'algo': 'NLOPT_SLSQP'}



.. GENERATED FROM PYTHON SOURCE LINES 67-69

Post-process the results
------------------------

.. GENERATED FROM PYTHON SOURCE LINES 69-72

.. code-block:: default

    scenario.post_process("OptHistoryView", save=False, show=False)
    # Workaround for HTML rendering, instead of ``show=True``
    plt.show()



.. rst-class:: sphx-glr-horizontal


    *

      .. image-sg:: /examples/scalable/images/sphx_glr_plot_scalable_param_mdf_002.png
         :alt: Evolution of the optimization variables
         :srcset: /examples/scalable/images/sphx_glr_plot_scalable_param_mdf_002.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /examples/scalable/images/sphx_glr_plot_scalable_param_mdf_003.png
         :alt: Evolution of the objective value
         :srcset: /examples/scalable/images/sphx_glr_plot_scalable_param_mdf_003.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /examples/scalable/images/sphx_glr_plot_scalable_param_mdf_004.png
         :alt: Distance to the optimum
         :srcset: /examples/scalable/images/sphx_glr_plot_scalable_param_mdf_004.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /examples/scalable/images/sphx_glr_plot_scalable_param_mdf_005.png
         :alt: Hessian diagonal approximation
         :srcset: /examples/scalable/images/sphx_glr_plot_scalable_param_mdf_005.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /examples/scalable/images/sphx_glr_plot_scalable_param_mdf_006.png
         :alt: Evolution of the inequality constraints
         :srcset: /examples/scalable/images/sphx_glr_plot_scalable_param_mdf_006.png
         :class: sphx-glr-multi-img






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.. _sphx_glr_download_examples_scalable_plot_scalable_param_mdf.py:

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